1. Field of the Invention
The present invention relates to an apparatus for extracting device parameters from semiconductor devices.
2. Description of the Related Art
An electronic circuit simulation is made by extracting operating parameters from a device model so as to imitate their real-life behaviors. The drain current of a device model using MISFET's (metal-insulator-semiconductor field-effect transistor) is given by the relation: EQU I.sub.D =f(p.sub.1, . . . , p.sub.N ; V.sub.D, V.sub.G, V.sub.SUB) (1)
where V.sub.D, V.sub.G and V.sub.SUB are the drain voltage, gate voltage and substrate voltage, respectively, using the source terminal as a reference potential, and p.sub.1, . . . , p.sub.N are physical values such as carrier mobility, saturation speed, gate length, channel width and so forth. Of these, directly measurable parameters such as gate length are given in advance of the simulation. In the case of high precision models, several tens of parameters are extracted. If the drain current of a measured device is given by: EQU I.sub.D =g(V.sub.D, V.sub.G, V.sub.SUB) (2)
the usual parameter extraction involves selecting parameters p.sub.1 .about.p.sub.N such that they substantially correspond to real-life values in the full range of the voltages V.sub.D, V.sub.G and V.sub.SUB. Specifically, the parameters p.sub.1 .about.p.sub.N are selected so that square error E=.SIGMA.(f.sub.i -g.sub.i).sup.2 has a minimum value (where f.sub.i and g.sub.i are the i-th measured voltages of Equations (1) and (2), respectively), using an iterative method of programmed algorithm by tentatively giving initial values for p.sub.1 .about.p.sub.N and recursively updating the parameters until the size of changes becomes insignificant. However, the extracted parameters often deviate largely from the values which can be expected. For example, if a set of parameters is extracted from a device model of gate length L.sub.1, a change of gate length to L.sub.2 would result in a complete loss of agreement with the performance of an actual device of gate length L.sub.2. This arises from the fact that, even though the operating characteristics of a device model do not perfectly fit to the real-life characteristics, a parameter extraction has been performed without taking into account their subtle differences.
To alleviate this discrepancy problem, some important parameters are measured separately. One example is to use a MISFET model having a relatively large gate length L and a relatively large channel width W and measure the carrier mobility .mu..sub.EFF according to the following relation: EQU I.sub.D =(W/L).mu..sub.EFF C.sub.ox (V.sub.G -V.sub.TH)V.sub.D ( 3)
where V.sub.TH is the threshold voltage and C.sub.ox is the capacitance of the gate oxide film per unit area. Since Equation (3) can be precisely established if V.sub.D &lt;&lt;V.sub.G -V.sub.TH, measurements made under appropriate conditions allow the parameter .mu..sub.EFF to be determined independently of other parameters. Another example is the derivation of an offset value .DELTA.L=L-L.sub.EFF (where L.sub.EFF is the effective channel length) and the derivation of a parasitic resistance R.sub.EX between source and drain, as disclosed in Japanese Patent Publication (Tokkaisho) 54-26667, by measuring source-drain resistances of several device models having particular gate lengths by applying low drain voltages.
Precise measurement of the parameters .DELTA.L and R.sub.EX significantly alleviates the discrepancy problem, particularly for low drain bias conditions (V.sub.D &lt;&lt;V.sub.G -V.sub.TH, so called `linear region`). However, the device characteristics under the high drain bias conditions (saturation region), which are usually more important than the linear region for digital applications, are still difficult for the model to correctly reproduce. This is due to the lack of accurate data on the distance between the source and the pinch-off point of the device. The pinch-off point is a point beyond which the carrier enters a pinch-off region where it is pulled off to the drain by a high intensity field. As a result, the drain current of a MISFET in the saturation region is determined by the distance between the source and the pinch-off point, rather than the source-to-drain distance of the device, which is called `effective channel length`. It is known that the effective channel length is not equal to the gate length and the difference between them is of a constant value that can be universally applied to all MISFET devices fabricated by a common manufacturing process. However, no methods have hitherto been available to precisely determine the universal difference value between the gate length and the source-to-pinch-off point distance.